EMPIRE: a highly parallel semiempirical molecular orbital program: 1: self-consistent field calculations

摘要

We use the expression “semiempirical molecular-orbital theory” in the following only for MNDO-like NDDO-based molecular-orbital (MO) techniques [1] such as MNDO [2], MNDO/c [3], MNDO/d [4–7], AM1 [8], AM1~* [9–14], RM1 [15], PM3 [16, 17], and PM6 [18]. These methods represent the currently accepted norm for semiempirical MO calculations, although more accurate methods that include orthogonalization corrections are also available [19–21]. The major advantage of such techniques is that they provide quite accurate one-electron properties [1] at a fraction (generally estimated to be at most 10~(?3)) of the computational cost of techniques such as density-functional theory (DFT) or ab initio calculations. Because of the dominant diagonalization of the Fock-matrix, semiempirical MO calculations are generally considered to scale with O(N~3), where N is the number of atomic orbitals. Linear scaling can be approached quite easily by using either divide and conquer (D&C) [22–24] or localized molecular orbital (LMO) [25] techniques, although neither is suitable for very extensively conjugated systems such as those typically encountered in molecular electronic devices [26]. However, the current generation of linear scaling semiempirical MO programs is quite adequate for calculating wavefunctions for most protein-sized molecules. A practical upper limit on desktop hardware seems to lie around or slightly below 20,000 atoms [27]. Because the calculations are fast, relatively little attention has been paid to efficient parallel computation and most current programs are essentially scalar in nature. A parallel version of MNDO94 was described as long ago as 1995 [28]. The D&C codes are in principle moderately parallel but parallel performance has not until now been an important issue for semiempirical MO calculations. More recently, an SCF approach for threedimensional condensed-phase systems has been introduced that has the potential to be able to perform calculations on millions of atoms with NDDO [29].